Department Mathematik
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Prof. Dr. Markus Land

Mathematisches Institut der Universität München
Theresienstr. 39
D-80333 München

Email: Markus.Land@mathematik.uni-muenchen.de

Tel:   +49 (0)89   2180 4415
Fax:  +49 (0)89   2180 4466
Büro: Block B, 4. Stock, 416

Arbeitsgruppe Algebraische Geometrie



I work in algebraic topology and homotopy theory with main current interest in algebraic and hermitian algebraic K-theory and their relation to L-theory and the topology of manifolds.

Preprints

  • A survey on operator K-theory via homotopical algebra
    Joint with Ulrich Bunke and Ulrich Pennig.

  • On the K-theory of pushouts
    Joint with Georg Tamme.

  • Remarks on chromatically localised hermitian K-theory

  • Paschke duality and assembly maps
    Joint with Ulrich Bunke and Alexander Engel.

  • A stable \infty-category for equivariant KK-theory
    Joint with Ulrich Bunke and Alexander Engel.

  • Hermitian K-theory for stable infinity-categories III: Grothendieck-Witt groups of rings
    Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.

  • Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivity
    Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.

    • Publications

  • Purity in chromatically localized algebraic K-theory
    J. Amer. Math. Soc. Published electronically: February, 1. 2024.
    Joint with Akhil Mathew, Lennart Meier, and Georg Tamme.

  • L-theory of C*-algebras
    Proc. London Math. Soc. (3). 127 (2023), no. 5, 1451--1506.
    Joint with Thomas Nikolaus and Marco Schlichting.

  • Gabber rigidity in hermitian K-theory
    Proceedings of the Royal Society of Edinburgh Section A: Mathematics (Ranicki memorial issue), to appear

  • Hermitian K-theory for stable infinity-categories I: Foundations
    Selecta Math. (N.S.) 29 (2023) no. 1.
    Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.

  • Reducibility of low dimensional Poincare duality spaces
    Münster J. of Math. 15 (2022) 47--81

  • Topological 4-manifolds with 4-dimensional fundamental group
    Glasgow Math. J. 64, (2022), no. 2, 454-461.
    Joint with Daniel Kasprowski.

  • Topologically flat embedded 2-spheres in specific simply connected 4-manifolds
    2019--20 MATRIX annals, 111-116, MATRIX Book Ser., 4, Springer, Cham, 2021.
    Joint with Daniel Kasprowski, Peter Lambert-Cole, and Ana G. Lecuona.

  • Connected sum decompositions of high-dimensional manifolds
    2019--20 MATRIX annals, 5-30, MATRIX Book Ser., 4, Springer, Cham, 2021.
    Joint with Imre Bokor, Diarmuid Crowley, Stefan Friedl, Fabian Hebestreit, and Daniel Kasprowski.

  • On the homotopy type of L-spectra of the integers
    J. Topol. 14, (2021), no. 1, 183--214.
    Joint with Fabian Hebestreit and Thomas Nikolaus.

  • A vanishing theorem for tautological classes of aspherical manifolds
    Geometry & Topology 25-1 (2021), 47--110.
    Joint with Fabian Hebestreit, Wolfgang Lück, and Oscar Randal-Williams.

  • On the K-theory of pullbacks
    Ann. of Math. (2) 190 (2019), no. 3, 877--930.
    Joint with Georg Tamme.

  • On the relation between K- and L-theory of C*-algebras
    Math. Ann. 371 (2018), no. 1-2, 517--563.
    Joint with Thomas Nikolaus.

  • Localization of cofibration categories and groupoid C*-algebras
    Algebr. Geom. Topol. 17 (2017), no. 5, 3007--3020.
    Joint with Thomas Nikolaus and Karol Szumilo.

  • Stable classification of 4-manifolds with 3-manifold fundamental group
    J. Topol. 10, (2017), no. 3, 827--881.
    Joint with Daniel Kasprowski, Mark Powell, and Peter Teichner.

  • The analytical assembly map and index theory
    J. Noncommut. Geom. 9 (2015), no. 2, 603--619.

    • Book

  • Introduction to Infinity-categories
    Compact Textbooks in mathematics, Birkhäuser, Cham, 2021.